Jeff, list: This is an emendation to my last post. It could be easily mis-interpreted. The first commentary paragraph should read:
> JLRC: My comment was directed toward the role of semantics in philosophy and > the cyclic nature of dictionary definitions in general, as well as the deep > tensions among philosophers using the same terms with radically different > meanings. Say, for example, the meaning of “category” or of “phenomenology”. > I would venture to conjecture that the very life blood of philosophical > thought is to propose new meanings for terms. For example, the responses of > Fitche and Schelling to Kant’s views of the role of the “I” in > transcendentalism. New philosophical constructs may be constructed and > exposed within the framework of new symbol SYSTEMS grounded in scientific > measurements, e.g., the role of genetic symbols in the in practice of > medicine and law. In the case of chemistry, the interpretation of the meaning > of traditional chemical symbols for matter (such as gold, lead, zinc, and > other metals) was drastic modified in order to incorporate the meaning of > Volta experiments demonstrating that pure chemical elements could generate a > flow of electricity (these physical constructs are termed batteries today.) > More bluntly stated, the phrase falling “down the rabbit hole” is a metaphor > that is, in essence, philosophically, ontologically and epistemologically, > illiterate. Cheers Jerry On Aug 24, 2014, at 11:56 AM, Jerry LR Chandler <[email protected]> wrote: > Jeff: > > Excellent post. Your contributions to the discussions here are among the > best. That being said, I chose to re-name the thread so that your > contribution is identified with your contributions. > > I will attempt to counter several of your arguments over the course of > several responses. (I am currently in the midst of a 6 week business, > vacation, and family trip so that it is necessary to partition your message > into manageable chunks.) > > On Aug 23, 2014, at 9:26 PM, Jeffrey Brian Downard <[email protected]> > wrote: > >> Jerry says: "My personal feeling about your exposition is that such a view >> of material and formal categories leads one into an extra-ordinarily deep >> philosophical morass from which you may never emerge." >> >> At the Congress, several people expressed a worry about falling "down the >> rabbit hole" when studying Peirce. > > JLRC: My comment was directed toward the role of semantics in philosophy and > the cyclic nature of dictionary definitions in general, as well as the deep > tensions among philosophers using the same terms with radically different > meanings. Say, for example, the meaning of “category” or of “phenomenology”. > I would venture to conjecture that the very life blood of philosophical > thought is to propose new meanings for terms such that new mental constructs > may be constructed and exposed within the framework of new symbol SYSTEMS > grounded in scientific measurements, e.g., chemistry. > More bluntly stated, the phrase falling “down the rabbit hole” is a metaphor > that is, in essence, philosophically, ontologically and epistemologically, > illiterate. >> >> Despite your warnings, I will have to trust my own judgment in determining >> when it makes sense for me to press on when it comes to the more challenging >> texts and arguments. > > JLRC: I fully and completely support your decision. Your original, > thought-provoking and well-structured message are welcomed. In fact, I would > love to listen to your lectures on environmental law where both there legal > content and for there philosophical content and the interlacing of the two. > I would strongly encourage other posters to this list serve to adopt your > approach! > > >> My conviction is that Peirce often is trying to teach us how to employ >> specific methods in doing philosophy, and that we'll struggle in our >> attempts to understand him so long as we lack the experience and skills he >> possessed. I don’t know about you, but this puts me in a tough position, >> because I seem to lack much of his experience and skills. While Peirce >> tried to put many things in the simplest possible terms, he often takes it >> for granted that the reader will "actively think" and draw on his sentences >> as "so many "blazes to enable him to follow the track of the reader's >> thought." (EP, 301) > > JLRC: I find this paragraph to be non-pragmatic from the perspective of > intellectual history. Pragmatically, the cultural milieu of 1839-1914 will > never be repeated, the rhetorical meanings of the context of language usage, > especially scientific terminology, was irreversibly dissolved in the onward > (and turbulent!) flows of time itself. In other words, "blazes to enable him > to follow the track” are of limited value because, over the past century, the > cultural milieu has changed the deep structures of the pathways of human > communication. >> >> >> Reading Peirce presents a challenge. As many scholars have pointed out, he >> was a remarkably talented logician, and he possessed an intimate familiarity >> with the mathematics of the 19th century and its larger history. What is >> more, he was a practicing scientist who had a rich understanding of how to >> do and not merely read chemistry, astronomy, classificatory biology, and >> geodesy. In addition to being a special scientist working in multiple >> fields, he had a synoptic sense of the history philosophy and the conceptual >> landscapes represented by different philosophical systems—along with a rich >> appreciation of the different worldviews that philosophers might try to >> explore. Above all, he was a student of methodology, and his aim was to >> develop a systematic method for improving the methods of inquiry. > > JLRC: Yes! But, pragmatically, these sciences, during the past century, > have continued their paths of inquiry, reforming and reformatting the “horse > and buggy” days to the space age. By introducing new terms and new forms of > logic, the modern cultural context of scientific semantics bear only a faint > resemblance to the thoughts of CSP. Equally pragmatically, I would > conjecture that human emotions and human behaviors toward one-another have > not changed substantially during the past century or centuries. Efforts to > disentangle the changing from the non-changing is a fundamental challenge to > any student of the history of semantic categorization and to the meaning of > the formal title of this thread, "[PEIRCE-L] Phaneroscopy, iconoscopy, and > trichotomic category theory” > > So, the questions to you Jeff, is, how will your approach to categorization > address the differences between the "“horse and buggy” days and the > scientific categorizations of 2014? > Will your approach differentiate between the unchanging and the changing, > the historical rhetoric and the current usage, the stable and the emergent? > (I am not asking about rabbit holes, I am asking about your personal approach > to coping with categories as both historical and current objects of thought.) > > This ends the first portion of my response. We will proceed into a modern > view of K.S. in a future post, not as a Gospel from Saint Charles, but from > the 21st Century view of categories. > > (Germane, but as an aside, I just returned from Germany, known for what is > asserted to be first food safety law (1516?) and its success in protecting > the quality of beer over the past nearly 4 centuries!) > > Cheers > > Jerry > >> >> Turning from these remarks about the difficulties one faces in trying to >> understand Peirce's views--especially the more difficult arguments expressed >> in the more challenging texts--to the task of reconstructing some of >> Peirce's arguments in the text of "New Elements (Kaina Stoicheia)", let's >> take a look at the text itself. There are three main sections. The first >> contains biographical remarks about the textbook he wrote on the logic of >> mathematics--taking topology, projective geometry and metrical geometries as >> its subject matter. The second contains a statement of the distinction >> between definitions, postulates, axioms, etc. The third, which is the >> longest section, is divided into 4 sub-sections. You quote from the fourth >> and longest of these subsections. >> >> What is Peirce doing in the passage you've quoted? It is possible that we >> are reading the text somewhat differently. Let me provide a few of comments >> about what he is doing in the pages leading up to the passage you've quoted >> so that we might clarify some of the differences in our approaches. I note >> that you've quoted the passage, but you've said precious little about what >> you think is going on here. You refer to an earlier post by Clark, so >> perhaps I could turn to what he says at some later time in an attempt to >> understand your remarks. >> >> So, in parts I and II, Peirce starts by referring to his own work on the >> logic of mathematics. By the fourth part of section III, he has moved from >> a discussion of speculative grammar and critical logic to a series of >> examples drawn from the theoretical and the practical sciences. You seem to >> be particularly interested in his remarks about the various specific uses of >> the concepts of cause and effect, including internal and external causes, >> along with material, formal, efficient and final causes. He has an >> exceptionally long paragraph on the topic starting on page 313 and ending on >> 316. The point of this little foray on the different causes is not to >> argue for big metaphysical conclusions. He's made those arguments >> elsewhere. And, he says as much: “Yet I refuse to enter here upon a >> metaphysical discussion.” (EP, ) >> >> As he points out in the opening sentence of this paragraph, everything he >> says here is designed to clarify the distinction between a proposition and >> an argument. His goal, I think, is to illustrate how we should go about >> classifying different acts of cognition (e.g., as an act of interrogating, >> affirming or arguing) and then ascertaining the nature of those acts. So, >> the question is something like this: >> >> 1) If the act is one of affirming an assertion, then what is involved in >> affirming that the proposition true? >> >> Or this: >> >> 2) If the act is one of arguing for a conclusion from a set of premisses, >> then what is involved in affirming that the argument is valid? >> >> He is also asking the question: How can we put our questions to nature and >> get a reasonable answer? That is, how can we find out what is really the >> case? These sound like questions of metaphysics, but he is focusing on a >> set of questions that surface in the theory of logic. Namely, what >> hypotheses concerning the nature of what is real should we adopt for the >> sake of understanding the validity of deductive, inductive and abductive >> inferences? He has argued that we need, for the sake of making valid >> deductive arguments, to adopt a nominal definition of the real. He sees that >> induction and abduction requiring richer hypotheses concerning the real. >> >> Here are some things that he says about the hypotheses that are required for >> the sake of making valid abductive inferences: >> >> “Abduction . . . is the first step of scientific reasoning, as induction is >> the concluding step. >> In abduction the consideration of the facts suggests the hypothesis. In >> induction the study of the hypothesis suggests the experiments which bring >> to light the very facts to which the hypothesis had pointed. The mode of >> suggestion by which, in abduction, the facts suggest the hypothesis is by >> resemblance, -- the resemblance of the facts to the consequences of the >> hypothesis. The mode of suggestion by which in induction the hypothesis >> suggests the facts is by contiguity, -- familiar knowledge that the >> conditions of the hypothesis can be realized in certain experimental ways. >> >> I now proceed to consider what principles should guide us in abduction, or >> the process of choosing a hypothesis. Underlying all such principles there >> is a fundamental and primary abduction, a hypothesis which we must embrace >> at the outset, however destitute of evidentiary support it may be. That >> hypothesis is that the facts in hand admit of rationalization, and of >> rationalization by us. That we must hope they do, for the same reason that a >> general who has to capture a position or see his country ruined, must go on >> the hypothesis that there is some way in which he can and shall capture it. >> We must be animated by that hope concerning the problem we have in hand, >> whether we extend it to a general postulate covering all facts, or not. >> >> We are therefore bound to hope that, although the possible explanations of >> our facts may be strictly innumerable, yet our mind will be able, in some >> finite number of guesses, to guess the sole true explanation of them. That >> we are bound to assume, independently of any evidence that it is true. >> Animated by that hope, we are to proceed to the construction of a >> hypothesis.” (CP 7.218-19) >> >> Given the fact that the primary subject matter of the “New Elements” essay >> is the normative science of logic, let us ask: what are the data (i.e., the >> observations) for generating hypotheses in logic and then putting them to >> the test? As we seek an answer the question, I believe that we need to >> focus our attention on the “data” part of the equation. As he says, “the >> logician has to be recurring to reexamination of the phenomena all along the >> course of his investigations.” (EP, 311) >> >> In the paragraphs leading up to his remarks about atomic weights, he >> considers the following examples: a psychologist studying the experience of >> déjà vu, a logician studying of the experience of similarity and >> resemblance, a seamstress buying fabric from a shopkeeper, a homeowner >> buying a piece of furniture, and a chemist studying the weight of gold. >> What is the point of these examples? Much of Peirce’s attention is fastened >> on the question of how we should arrive at a more scientific understanding >> of the conditions for making measurements. How should we measure a >> psychological feeling, or a length of silk, or a the size of a piece of >> furniture, or the chemical weight of an element—or the degree to which one >> feeling (or other idea) is, logically speaking, similar to an another. >> >> In some “comments on “The Basis of Pragmatism in the Normative Sciences,” I >> forwarded the claim that Peirce’s phenomenology is, at least in part, an >> attempt to answer the following question: what are the formal features in >> experience that are necessary for us to draw valid synthetic inferences from >> our observations? This is not an easy question to answer. We’re looking >> for an answer because we want to understand how it is possible to put the >> qualities we’ve observed in a transitive ordering and make comparisons based >> on the degree to one resembles or does not resemble another. I’d like to >> add the following to what I’ve said thus far: discovering the formal >> conditions for putting things in such a transitive order and comparing them >> are essential aspects of what is needed to measure them. >> >> The point he is making about using a yard stick to measure length is >> analogous to the point he is making about using a standard for measuring the >> chemical weight of gold. In order to make measurements of length, we use >> something that is like a rigid bar that can be moved up and down the thing >> we are measuring (so that the finite length of the bar does not matter for >> purposes of making the measurements). The remark that caught my attention >> is where he says that our theory of measurement is based on the idea that we >> need something that can serve as a more universal standard. In an effort to >> make our standard more universal, scientists have designated one particular >> bar in Westminster as the object to which our concept of yard refers. In >> order to determine whether or not any other yardstick we might use will lead >> us into error, we can—as a matter of principle—compare it to the protypical >> standard in Westminster. >> >> Is this the best way to fix the reference for the concept of a yard? Peirce >> thinks it is not the best way to remove some of the errors that will crop up >> in the process of making measurements of length. Instead of relying on a >> single prototype sitting in a case in Westminster, we should rely on an >> average taken from a number of different bars made of different materials >> and kept under different conditions (e.g., at different ranges of >> temperature). We use the concept of yard in such a way that it refers to >> the mean length of them all. This is the same kind of thing that a >> biologist does when she compares a number of different specimens and draws >> up a conception of a “type-specimen” as a kind of typical thing that has a >> normal size and shape. >> >> What is the weight of gold? In saying that it is an elementary chemical >> substance having a particular atomic weight of about 197 ¼, we are relying >> upon some kind of standard in making the comparison. The standard, of >> course, is the atomic weight of hydrogen, which is taken to have a weight of >> 1. What is it to say that the weight of hydrogen is 1 unit? His answer is >> that, in comparison to air, it is about 14 ½ times lighter. >> >> In this passage, is Peirce making some kind of metaphysical point about the >> deeper “logic” of the chemical elements? I don’t think so. Rather, he is >> making a point about what is needed to make comparisons between things—and >> then he is asking what is needed to set up a standard for measuring those >> things. The system of measurement set up by Dalton in 1803 was a relative >> scale that used the weight of hydrogen as the base unit. Technically >> speaking, scientists could say that the mass of hydrogen was exactly one >> only because it was the serving as the base unit of measurement in a >> relative scale. It would not serve the goals of the scientists to say that >> the concept of the weight of hydrogen refers to protypical sample stored in >> a glass case in Westminster. Rather, the weight of hydrogen, like the length >> of a yard, should be taken to refer to a mean over many observations of the >> relative weights of gold, carbon, hydrogen and other elements. >> >> What does this have to do with the normative theory of logic? I believe >> that it bears on logic in two ways. First, I believe that an analysis of >> the things we observe—in chemistry, biology, the selling of fabric, >> etc.—requires us to examine the underlying grounds for making measurements >> of the various phenomena. We can draw on mathematics, phenomenology and >> logic in order to deepen our understanding of what is necessary to apply one >> or another kind of measurement to a given kind of phenomena that has been >> observed in one or another of the practical or theoretical sciences. >> Second, this kind of question surfaces when we ask what the standards are >> for analyzing the phenomena we’re drawing on in the theory of logic. Peirce >> says as much in his discussion of what is needed to make something as simple >> as a comparison between two qualities of feeling. Take, for instance, a >> comparison between two experiences of the color of blue. In the hospital >> room where I’m sitting with my daughter, there is a stool and a sheet that >> have just about the same hue. From this point on, I will probably refer to >> this shade of color as “hospital blue.” When I compare the intensity of the >> color I experience when looking at the stool with the color I experience >> when looking at the sheet, it seems to me that the color of the stool is >> remarkably more intense than the color of the sheet. The two objects are >> across the room from each other, so all I can do is to compare the intensity >> of the one with my memory of the intensity of the other. What are my >> grounds for making such a comparison? >> >> One of the points Peirce is making at this point in subsection 4 is that the >> comparison of the intensity of two experiences of the quality of blue is >> something that is “measured chiefly by aftereffects.” (EP, 320) He is >> laboring over this point, I believe, because he is keenly interested in set >> of related issues. Consider, for instance, the following questions: >> >> 1) What is the standard that we can use when comparing the feeling that an >> argument is a good inference to the feeling that an argument is an invalid >> inference? Isn’t this similar in some respects to comparing the intensity >> of a one experience of a feeling of blue to another feeling of blue? Isn’t >> it different in other respects? >> >> 2) Once we have formed a class of sample arguments that we take to be good >> and a class that we take to be bad, what kind of measurements can be made >> when comparing these classes? At the very least, we can apply a nominal >> scale in saying that they are labeled as different classes. For the sake of >> the logical theory, however, we need a stronger standard of measurement, >> don’t we? >> >> 3) What is the standard for making the comparison of the goodness or >> badness of an argument? Should we take it to be a prototypical argument that >> appears to be beyond criticism? Perhaps we should take an argument, such as >> a cogito argument, or an ontological argument for God’s reality, or an >> argument for the indubitability of the axioms of logic as a prototype, and >> then place one or another of these arguments in a glass case in Westminster. >> I suspect that this would fail to serve the purpose we have in removing >> possible errors from our measurements of the goodness or badness of any >> given argument. >> >> How can the examples of measuring silk against a yardstick, comparing >> biological specimens to a “type-specimen”, and comparing the weight of >> carbon and gold to hydrogen help us think more clearly about the grounds we >> having for comparing arguments and saying that one class contains a sample >> of good inferences and that another class contains a sample of bad >> inferences. In making such comparisons, we need something more than just a >> nominal assignment of the term ‘good’ to one class and ‘bad’ to another. >> Having said that, don’t we need more than an ordinal scale that enables us >> to make relative comparisons of goodness and badness? How might we arrive >> in our theory of logic at a standard of measuring the validity of inferences >> that is richer than a nominal or ordinal scale? After all, we are relying >> on our standards for comparing arguments for the sake of arriving at >> conclusions about what, really, is true and false. >> >> These are the kinds of questions that I’m particularly interested in trying >> to answer. My hunch is that, rabbit hole or not, Peirce is pointing us to >> the resources needed to answer these kinds of questions. As he points us in >> a specific direction, however, he is assuming that we will "actively think" >> and draw on his sentences as "so many blazes to enable him to follow the >> track of the reader's thought." The real danger is not one of following >> the blazes and heading down the rabbit hole. Rather, it is one of sticking >> with our personal assumptions and convictions in such a fashion that we make >> ourselves impervious to the fruitful suggestions that are around us and, in >> doing so, fail to see that we are sitting in a hole of our own making with >> no sense of which direction is up and which is down. >> >> That, at least, is my abiding worry. Hopefully, it is one that will spur me >> to active inquiry. >> >> --Jeff >> >> >> Jeff Downard >> Associate Professor >> Department of Philosophy >> NAU >> (o) 523-8354 >> ________________________________________ >> From: Jerry LR Chandler [[email protected]] >> Sent: Friday, August 22, 2014 3:35 PM >> To: Peirce List >> Cc: Jeffrey Brian Downard >> Subject: Re: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category >> theory >> >> Dear Jeff: >> >> Thank you for your exposition on your views on the relations between >> material and formal categories. >> (From your post below) >> First off, if things are sounding mystical to your ears, I hope it is a by >> product of the richness of the ideas Peirce is examining--and not a >> by-product of the comments I'm offering. >> >> Your hopefulness is partially realized. And partially not. >> >> Your may recall Clark’s perceptive’s postings from Kainia Stoichia on CSP >> views on causality. In subsequent sentences, CSP gives a crisp example of >> his deductions about relations between gold (as a relative weight) when >> compared to hydrogen and then to air. >> "What is gold? It is an elementary substance having an atomic weight of >> about 197¼. In saying that it is elementary, we mean undecomposable in the >> present state of chemistry, which can only be recognized by real reactional >> experience. In saying that its atomic weight is 197¼, we mean that it is so >> compared with hydrogen. What, then, is hydrogen? It is an elementary gas 14¼ >> times as light as air. And what is air? Why, it is this with which we have >> reactional experience about us. The reader may try instances of his own >> until no doubt remains in regard to symbols of things experienced, that they >> are always denotative through indices; such proof will be far surer than any >> apodictic demonstration. From KS. >> >> This crisp example of material and formal categories (and the logical >> phenomena inferred by mathematics) about material categories is worthy of >> careful study. He presents a logic of relatives. Classification of >> categories inevitably brings forth issues of causality, Aristotelian or >> otherwise, which he illustrates. You may find it useful to contrast this >> example with other direct examples from biology or medicine as you pursue >> your thinking about these matters. >> >> My personal feeling about your exposition is that such a view of material >> and formal categories leads one into an extra-ordinarily deep philosophical >> morass from which you may never emerge. For me, the choice of rhetorical >> terms in your exposition leads not to calculations but to a Luciferic >> network of semantic entanglements. >> >> Thanks again for clarifying your thoughts. >> >> Cheers >> >> Jerry >> >> >> >> >> >> On Aug 22, 2014, at 1:39 AM, Jeffrey Brian Downard >> <[email protected]<mailto:[email protected]>> wrote: >> >> On Wed, Aug 20, 2014 at 3:05 PM, Jeffrey Brian Downard >> <[email protected]<mailto:[email protected]><mailto:[email protected]>> >> wrote: >> Hi Jerry, List, >> >> First off, if things are sounding mystical to your ears, I hope it is a by >> product of the richness of the ideas Peirce is examining--and not a >> by-product of the comments I'm offering. >> >> To a large degree, the answers to the questions you are trying to raise are >> going to be found in the larger story that is articulated in the theory of >> semiotics. At this point, I am trying to offer some comments on some of >> Peirce's explanations and definitions as a kind of run up to the >> phenomenological categories--and especially the distinction between the >> formal and material aspects of those categories. The general suggestion I'm >> making is that Peirce is not providing two entirely separate lists of the >> categories, one formal and that other material. Rather, there is a close >> connection between the two even if they do not, in experience, match >> perfectly because our experience of the material categories of quality, >> brute fact and mediation is always so richly complex. My general suggestion >> may seem controversial because some interpreters seem to be offering a >> different reading of the relevant texts. >> >> Confining myself to the subject of the phenomenological categories and the >> role of mathematics in informing our understanding of the essential formal >> elements of the monad, dyad and triad, I do take Peirce to be offering an >> account of the elements needed for setting up the frameworks necessary for >> referring to grounds, objects and interpretants. One might call them three >> interrelated "frames of reference." >> >> What do the signs that we use in mathematics refer to? Much depends upon >> whether we are using the signs to seeks answer to questions in pure or >> applied mathematics. Let's consider the case of pure mathematics. What do >> the signs used in topology refer to? In the account he offers in the New >> Elements, the key operations for setting up a system of mathematical >> diagrams are those of generation and intersection. These are the operations >> used to generate a line by moving a particle from a point, or for >> determining the location of a point on a line by intersecting it with >> another line. >> >> As we try to understand the conditions that make it possible for the >> different representations to refer, we'll need to be clear in identifying >> the representations we're talking about. It is one thing to ask: what does >> that particle in the diagram that is being moved refer to? It is another >> thing to ask, what does the symbol "particle" refer to? I hope it is clear >> that the conditions under which the symbol "particle" refers is dependent, >> in many respects, on the conditions under which the iconic particle that is >> draw on the page is able to refer. As a hypo-icon, the particle we move as >> we draw the line is remarkably rich as a sign. At any time in the act of >> drawing the line on the paper, there are qualisigns, sinsigns and legisigns >> working together so that the particle can function as a rich sign complex in >> a larger process of interpretation. What is more, the particle embodies the >> idea of a generator. That is, it embodies a more general rule that >> determines how we might generate innumerable other possible lines from the >> point. This is a more general rule that enables us to interpret the larger >> mathematical space in which the line is being constructed. It enables us to >> understand how one line my be transformed continuously to give us a line >> that is homeomorphic with the first, or how various kinds of discontinuities >> might be introduced to give us another different line altogether. >> >> I hope you can see that I'm trying to bracket some of the questions you've >> raised about the role of real things (i.e., chemical compounds, protein or >> DNA molecules, and the like) in serving as the grounds or objects to which >> one or another kind of representation might refer. I'm bracketing those >> questions for a reason. I'd like to keep the phenomenological analysis of >> the conditions under which the signs used in pure mathematics refer free >> from big metaphysical assumptions about what is really the case as a >> positive matter of fact. There is a long line of philosophers who have >> tried to import such metaphysical assumptions into their accounts of the >> reference and meaning of the signs used in math and formal logic (e.g., >> Mill, Quine, etc.), but Peirce is resisting this move--at least until we're >> ready to address questions in metaphysics. Once we are ready and we're >> using the methods appropriate for answering questions in metaphysics, we'll >> need to think about the real nature of an ideal system of mathematical >> definitions, hypotheses, theorems, etc., and what it is for that system to >> be real as a rich and consistent network of possible formal relations. >> >> --Jeff >> >> >> Jeff Downard >> Associate Professor >> Department of Philosophy >> NAU >> (o) 523-8354 >> ________________________________________ >> From: Jerry LR Chandler >> [[email protected]<mailto:[email protected]><mailto:[email protected]>] >> Sent: Tuesday, August 19, 2014 9:28 PM >> To: Jeffrey Brian Downard >> Cc: Peirce List >> Subject: Re: [PEIRCE-L] Phaneroscopy, iconoscopy, and trichotomic category >> theory >> >> Jeffrey: >> >> Your posts become increasingly mystical. >> >> This is not a judgement, merely an observation from a philosophy of >> mathematics perspective. >> >> At issue is how to you assign meaning to mathematical symbols. >> In particular, in light of K.S. and his comments on the meaning of number in >> the context of his description of gold? >> >> More to the point, does the meaning of mathematical symbols reside in >> mathematics itself or do the meanings refer to the reference systems for the >> symbol system, that is the application to a particular material reality, >> such as the atomic numbers? Or the sequence numbers for a genetic sequence? >> Or protein sequence? >> In yet other terms, does the concept of order infer a universal meaning or a >> meaning dependent on the nouns of the copulative proposition? >> >> Perhaps you can address these vexing issue? >> >> Cheers >> >> Jerry >> >> >> >> >> On Aug 19, 2014, at 8:28 PM, Jeffrey Brian Downard >> <[email protected]<mailto:[email protected]><mailto:[email protected]>> >> wrote: >> >> Gary F., Gary R., List, >> >> In an effort to think a bit more about the form/matter distinction as it >> applies to the phenomenological categories, let me add few comments about an >> explanation that Peirce provides concerning the mathematical form of a state >> of things. I'd like to add some remarks about this explanation because I >> think it offers us a nice way of responding to a concern Gary F. raised. >> Here is the concern: >> >> Gary F. says: "Jeff, I’m interested in your question, 'is there any kind of >> formal relation between the parts of a figure, image, diagram (i.e., any >> hypoicon) that does not have the form of a monad, dyad or triad?' . . . I >> confess that I have no idea how we would go about investigating that >> question." >> >> My initial response was: "The answer to the question involves the whole of >> Peirce's semiotic--and not just his account of the iconic function of signs. >> So Peirce is bringing quite a lot to bear on the question. For starters, >> however, I think we should consider the examples he thinks are most >> important in formulating an answer. What Peirce sees is that, in >> mathematics, the examples we need are as 'plenty as blackberries' in the >> late summer. (CP 5.483) What do you know, it is late August. Let's go >> picking." >> >> As a first stop on our way to the briar patch, let's consider the following >> definition from "The Basis of Pragmaticism in the Normative Sciences." >> >> "A mathematical form of a state of things is such a representation of that >> state of things as represents only the samenesses and diversities involved >> in that state of things, without definitely qualifying the subjects of the >> samenesses and diversities. It represents not necessarily all of these; but >> if it does represent all, it is the complete mathematical form. Every >> mathematical form of a state of things is the complete mathematical form of >> some state of things. The complete mathematical form of any state of things, >> real or fictitious, represents every ingredient of that state of things >> except the qualities of feeling connected with it. It represents whatever >> importance or significance those qualities may have; but the qualities >> themselves it does not represent." (EP, vol. 2, 378) >> >> Peirce suggests that this explanation is "almost self-evident." At this >> point in his discussion, however, he merely ventures the explanation as a >> "private opinion." I cite this passage because it bears directly on the >> question of how our understanding of the mathematical form of something such >> as a figure or diagram is supposed to inform our understanding of the formal >> categories of monad, dyad and triad (or, firstness, secondness, >> thirdness)--and how we might use those categories in performing a >> phenomenological analysis of something that has been observed. >> >> Peirce says that he has introduced this explanation in order to account for >> the emphatic dualism we find in the normative sciences. The dualism is >> especially marked in logic and ethics (e.g., true and false, valid and >> invalid, right and wrong, good and bad), but it is also found in aesthetics. >> As such, he is noticing a phenomena that has been widely observed to be a >> part of our common experience in thinking about how we ought to act and >> think, and he is getting ready to venture a hypothesis to explain what is >> surprising about the phenomena. The explanation of the dualism that follows >> might seem a bit hard to make out, but I think it is clear that this is what >> he is trying to do. >> >> That might have seemed a bit opaque, so let me try to restate the point. I >> think Peirce is drawing on an understanding of mathematical form for the >> sake of performing an analysis of a particular phenomenon that calls out for >> explanation. We need to see what it is in the phenomena (i.e., the dualism >> in the normative sciences) that really calls out for explanation. >> Otherwise, we will not have a clear sense of whether one or another >> hypothesis is adequate or inadequate to explain what needs to be explained. >> >> He says the following about his account of the mathematical form of a state >> of a things: "Should the reader become convinced that the importance of >> everything resides entirely in its mathematical form, he too, will come to >> regard this dualism as worthy of close attention?" >> >> Why does Peirce say that the importance of everything resides in its >> mathematical form? On my reading of this passage and what follows in the >> next several pages of the essay, I think he is developing the claim I >> asserted above. That is, every kind of formal relation that might be found >> between the parts of a figure, image, diagram and the space in which such >> things are constructed must have the form of what we are calling, in our >> phenomenological theory, a monad, dyad or triad. >> >> It might sound ridiculous to suggest that the dualism present in our >> experience of what is valid or invalid as a reasoning or what is right or >> wrong as an action can be clarified by using a mathematical diagram, such as >> a drawing on a piece of paper of two dots that we might count by saying >> "one' and "two," but he says that we shouldn't disregard such a suggestion. >> He has argued elsewhere that every observation we might make must involve >> some kind of figure or diagram--and the form of such a figure or diagram can >> be understood in terms of having the structure of a skeleton set (CP, >> 7.420-32), or a network figure (CP, 6.211), or some other kind of really >> basic mathematical structure. I refer to those particular mathematical >> structures because the first can be applied to things in our experience that >> are more discrete in character, and the second can placed over things more >> continuous in character. >> >> Do you buy his claim here? Does the "importance of everything reside in its >> mathematical form?" The argument he offers in the rest of section B is worth >> a look. >> >> --Jeff >> >> ----------------------------- >> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >> PEIRCE-L to this message. PEIRCE-L posts should go to >> [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but >> to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of >> the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . >
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